Question

the expression for the sum to n terms of some arithmetic sequence are given Below.
find the expression for the nth term of each:
I,n square + 2n
ii, 2n square+n​

Answer 1

Answer:

Step-by-step explanation:

1 ) sum = n²+2n

 common difference,d = 2xcoefficient of n²

                                   = 2x1

                                   = 2

 first term,f = sum of coefficients of all terms = 1+2 = 3

 nth term  = dn+(f-d)

                = 2n+(3-2)

                = 2n+1

               or

sum = n²+2n

sum of first term = first term = 1²+2x1 = 1+2 = 3

sum of first two terms = first term +second term = 2²+2x2

                                                 3 +second term = 4+4

                                                      second term = 8-3

                                                                           = 5

 common difference, d = 2nd term - 1st term

                                     = 5-3 = 2

 nth term  = dn+(f-d)

                = 2n+(3-2)

                = 2n+1

2) sum = 2n²+n

 common difference, d = 2xcoefficient of n²

                                   = 2x2 = 4

 first term,f = sum of all coefficients of n

                 = 2+1 = 3

 nth term = dn+(f-d)

               = 4n+(3-4)

               = 4n+(-1)

               = 4n-1

                                                   

               

Answer 2

Step-by-step explanation:

voila

btw just look at the pic

:)